From Impulse Transfer to Low-Thrust Transfer between Invariant ManifoldsReport as inadecuate




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1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans 2 CaGE - Control And GEometry LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris 3 LJLL - Laboratoire Jacques-Louis Lions

Abstract : In this work, a new method is developed to perform transfers that minimize fuel consumption between two invariant manifolds of periodic orbits in the Circular Restricted Three Body Problem. We start with an impulse transfer between two invariant manifolds to build an optimal control problem. This allows to choose an adequate fixed transfer time. Using the Pontryagin Maximum Principle, we formulate the resolution of the problem as that of finding the zero of a shooting function indirect method. We develop an algorithm that couples different kinds of continuations on cost, on final state, on thrust to improve robustness and to initialize the solver. We illustrate the efficiency of the method with numerical examples. Finally, we study the influence of time transfer with a numerical study which, thanks to a continuation on this parameter, shows that when transfer duration goes to zero, the control converges to the impulse transfer that we started with. To the best of our knowledge, it is the first time that such a result is obtained.

Keywords : invariant manifolds CRTBP optimal control continuation method low-thrust transfer





Author: Thomas Haberkorn - Emmanuel Trélat - Maxime Chupin -

Source: https://hal.archives-ouvertes.fr/



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